Related papers: Matrix Zakharov-Shabat Systems with Zero Diagonal …
In this announcement we present a general and new approach to analyzing the asymptotics of oscillatory Riemann-Hilbert problems. Such problems arise, in particular, in evaluating the long-time behavior of nonlinear wave equations solvable…
This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…
The matrix Schr\"odinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
We show that the study of the statistical properties of the scattering matrix S for quantum chaotic scattering in the presence of direct processes (charaterized by a nonzero average S matrix <S>) can be reduced to the simpler case where…
The Newton-Sabatier method for solving inverse scattering problem with fixed-energy phase shifts for a sperically symmetric potential is discussed. It is shown that this method is fundamentally wrong: in general it cannot be carried…
We consider right and left formulations of the inverse scattering problem for the Zakharov-Shabat system and the corresponding integral Gelfand-Levitan-Marchenko equations. Both formulations are helpful for numerical solving of the inverse…
We study one of multidimensional inverse scattering problems for quantum systems in a constant electric field, by utilization of the Enss-Weder time-dependent method. The main purpose of this paper is to propose some methods of sharpening…
In this paper, we consider the direct and inverse problem of scattering of time-harmonic waves by an unbounded rough interface with a buried impenetrable obstacle. We first study the well-posedness of the direct problem with a local source…
An easy to implement and powerful method for the solution of 3D scattering problems that can be well described by Helmholtz equation is presented. The matrix algebra used provides excellent stability versus the number of junctions as well…
In this paper we consider the direct scattering problem of obliquely incident time-harmonic electromagnetic plane waves by an infinitely long dielectric cylinder. We assume that the cylinder and the outer medium are homogeneous and…
We study the solvability of the general two-dimensional Zakharov-Shabat (ZS) systems with meromorphic potentials by quadrature. These systems appear in application of the inverse scattering transform (IST) to an important class of nonlinear…
We investigate a time harmonic acoustic scattering problem by a penetrable inclusion with compact support embedded in the free space. We consider cases where an observer can produce incident plane waves and measure the far field pattern of…
This work investigates the quantum transport in a narrow constriction acted upon by a finite-range transversely polarized time-dependent electric field. A generalized scattering-matrix method is developed that has incorporated a…
Different gauge copies of the Ablowitz-Kaup-Newell-Segur (AKNS) model labeled by an angle $\theta$ are constructed and then reduced to the two-component Camassa--Holm model. Only three different independent classes of reductions are…
We present a direct and simple method for the computation of the total scattering matrix of an arbitrary finite noncompact connected quantum graph given its metric structure and local scattering data at each vertex. The method is inspired…
We review some recent results on the theory of scattering and more precisely on the local Cauchy problem at infinity in time for some long range nonlinear systems including some form of the Schr"odinger equation. We consider in particular…
The action of a B\"acklund-Darboux transformation on a spectral problem associated with a known integrable system can define a new discrete spectral problem. In this paper, we interpret a slightly generalized version of the binary…
An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explicitly constructed in terms of the scattering data. The main…
Resonance phenomena are central to many quantum systems, where resonant states are typically characterized by pole singularities of the S-matrix. In this work, we employ the complex scaling method (CSM) in conjunction with exact WKB…